# Full text of "Analytical Mechanics"

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```CHAPTER XI. TINIPLANAR MOTION  OF A RIGID  BODY.
181. Angular Kinetic Reaction. — It will be remembered that in considering the equilibrium of rigid bodies the Law of Action and Reaction was divided into the following two sections :
To every linear action there is an equal and opposite linear reaction, or, the sum of all the linear actions to which a body or a part of a body is subject at any instant
vanishes.
= 0.
To every angular action there is an equal and opposite :mgular reaction, or, the sum of all the angular actions to which a body or a part of a body is subject at any instant
vanishes.
= 0.                                   Ao)
In Chapter VI the first section of the law was applied to particles in motion; but in order to do this the meaning of the terms " linear action" and " linear reaction" was -enlarged so as to include linear kinetic reactions as well as forces. In the present chapter the second section of the law will be applied to the motion of rigid bodies; but before doing this we must introduce another form of kinetic reaction, which we will call angular kinetic reaction. If we replace in the second section of the law the terms "angular action" and "angular reaction" by the terms "torque" and "angular kinetic reaction," we obtain the following form which is directly applicable to problems of rotation :
The sum of all the torques acting upon a rigid body .phis the angular kinetic reaction equals zero, or the
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